Problem: Simplify the following expression: $ a = \dfrac{-3}{2} - \dfrac{2q + 4}{9} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{-3}{2} \times \dfrac{9}{9} = \dfrac{-27}{18} $ Multiply the second expression by $\dfrac{2}{2}$ $ \dfrac{2q + 4}{9} \times \dfrac{2}{2} = \dfrac{4q + 8}{18} $ Therefore $ a = \dfrac{-27}{18} - \dfrac{4q + 8}{18} $ Now the expressions have the same denominator we can simply subtract the numerators: $a = \dfrac{-27 - (4q + 8) }{18} $ Distribute the negative sign: $a = \dfrac{-27 - 4q - 8}{18}$ $a = \dfrac{-4q - 35}{18}$